How do you calculate the shear in anchor rods?
The lateral forces acting on a structure will produce a horizontal reaction at the foundation level. For steel frames supported on base plates, a small horizontal force can be resisted by the friction between the plate and the underlying concrete. However, as the reaction increases, the friction may not be high enough to counteract the sliding force.
In this case, the base plate will tend to slide until the shear force is transferred to the anchor rods bearing laterally against the base plate. Base plates are usually fabricated with oversize holes to account for small misalignments of the anchor rods at the field, which would be expensive to fix. As a result, it’s very unlikely that all rods will bear against the base plate as in a perfect watch mechanism. The ACI recognizes this by allowing only the front rods to be effective for shear resistance purposes, unless all washers on the rods are welded to the base plate, in which case all rods would be effective, as shown in the picture below.
Design of anchor rods for shear.
Once the shear force has been calculated, the anchor rods should be checked for the following failure modes:
- Steel failure – This is a measure of the capacity of the anchor material. It shall be evaluated by calculations based on the properties of the anchor material and the physical dimensions of the anchor. The nominal steel strength is:
where Ase is the effective cross sectional area of the anchor. ASDIP Steel uses an internal database with the properties of different anchor sizes and materials.
- Concrete breakout – It assumes a failure forming a concrete cone based on a prism angle of 35 degrees. The CCD Method predicts the strength of a group of anchors by using a basic equation for a single anchor Vb, and multiplied by factors that account for the number of anchors, edge distance, eccentricity, cracking, etc.
The first factor has to do with the group of anchors producing the failure cone. The denominator is the breakout area of a single anchor, and the numerator is the group breakout area. The former can be easily calculated, but the latter may be quite difficult, since it depends on the geometric conditions of the support, as shown below.
A further complication arises when the plate is located less than 1.5 hef from three or more edges, in which case the effective depth hef needs to be recalculated. ASDIP Steel accurately calculates, for any support conditions, the breakout area Avc and the effective embedment depth hef and provides a graphic view, as shown below.
Similar to the anchor rods in tension, the calculation of the breakout failure mode in shear is particularly important since a concrete failure would be non-ductile, and therefore it should be avoided. To prevent this kind of failure, the Code allows the use of reinforcing steel across the failure surface. This anchor reinforcement, however, must be designed and detailed carefully so that the strength of the rebars can be developed at both sides of the failure surface.